Fluctuating Nematic Elastomer Membranes: a New Universality Class

TL;DR

This paper investigates the unique elastic properties of nematic elastomer membranes with broken rotational symmetry, revealing a new universality class characterized by singular elastic moduli and a stable fixed point in a theoretical D-dimensional framework.

Contribution

It introduces a theoretical analysis of nematic elastomer membranes, identifying a new universality class with anomalous elastic behavior near four dimensions.

Findings

Discovery of a new stable fixed point controlling membrane properties.

Elastic moduli vanish as a power-law with wavevector.

Finite bending rigidity persists at large scales.

Abstract

We study the flat phase of nematic elastomer membranes with rotational symmetry spontaneously broken by in-plane nematic order. Such state is characterized by a vanishing elastic modulus for simple shear and soft transverse phonons. At harmonic level, in-plane orientational (nematic) order is stable to thermal fluctuations, that lead to short-range in-plane translational (phonon) correlations. To treat thermal fluctuations and relevant elastic nonlinearities, we introduce two generalizations of two-dimensional membranes in a three dimensional space to arbitrary D-dimensional membranes embedded in a d-dimensional space, and analyze their anomalous elasticities in an expansion about D=4. We find a new stable fixed point, that controls long-scale properties of nematic elastomer membranes. It is characterized by singular in-plane elastic moduli that vanish as a power-law eta_lambda=4-D of a relevant inverse length scale (e.g., wavevector) and a finite bending rigidity. Our predictions are asymptotically exact near 4 dimensions.